Effect of deep levels on semiconductor carrier concentrations in the case of "strong" compensation

We analyze the carrier concentrations ($\equiv p$) resulting from both shallow and deep majority levels. We show that for comparable concentrations of shallow and of compensating levels, a small fraction of deep levels can decrease $p$ by orders of magnitude. Also, a quantitative criterion for obtaining semi-insulating material is derived, and implications for obtaining conducting wide-band-gap materials are discussed. Another result: a steep ("deep") slope of $\ln p$ vs $\frac{1}{T}$ can result even from small percentages of deep levels.